As discussed in chapter~\ref{sec:energy_profiling} energy profiles provide the base for
energy aware infrastructure. To enable such profiles metrics need to be defined. This
chapter explains the derivation of a suchlike metric.

\section{Focus}
The approach of this research is to be as generic as possible. It aims at being able
to include as much infrastructure as possible. To be able to define the metric, it
needs to be framed what the generically available data is.

\subsection{Racktivity PDU readings}
In most cases the readings of a \emph{Power Distribution Unit} (PDU) represent the
only uniform means of providing energy data within ICT-infrastructure.

Also the absence of \emph{802.3az (Energy-Efficient Ethernet)} results in nearly
constant energy consumption regardless of the utilization.

Examining one of the PDU outlets of the DAS-4 cluster, confirms this behavior. (see
figure~\ref{fig:outlet8w} and~\ref{fig:outlet8m}) 

\begin{figure}[!h]
 \begin{center}
  \includegraphics[width=\textwidth]{Figures/racktivity_outlet8_week.png}
  \url{http://145.100.102.81:22001/view/uva01/p/8?timespan=604800}
 \end{center}
 \caption{Week overview of the UvA DAS-4 ibswitch (PDU outlet 8)}
 \label{fig:outlet8w}
\end{figure}

\begin{figure}[!h]
 \begin{center}
  \includegraphics[width=\textwidth]{Figures/racktivity_outlet8_month.png}
  \url{http://145.100.102.81:22001/view/uva01/p/8?timespan=2592000}
 \end{center}
 \caption{Month overview of the UvA DAS-4  ibswitch (PDU outlet 8)}
 \label{fig:outlet8m}
\end{figure}

\section{Metric}
Parker and Walker~\citep{absolute-efficiency} introduced the logarithmic
\emph{absolute energy efficiency} metric (\ref{eq:energyefficiency}) that enables the
comparison of efficiency of ICT-architecture, ICT-hardware, etc.

\begin{equation}
	dB\varepsilon =
10log_{10}\left(\frac{Power/BitRate}{kTln2}\right)
	\label{eq:energyefficiency}
\end{equation}

Since GreenSONAR is an approach to standardize, this metric was chosen, as it provides
universal comparability irrespective to specific technology.

The derived definition~\ref{eq:energyefficiency_pp} extends $Power/BitRate$ by taking
into account the number of ports $N_{ports}$ and distributing the current energy
consumption $P_{total}$ evenly amongst them.  This value is put into relation to the
bandwidth left $Speed_{max}-Util_p*Speed_{max}$. If a port has a utilization of e.g.
80\%, it calculates to 20\% of the $Speed_{max}$ of that port in $bits/seccond$. The
division of energy consumption amongst the ports seems crude, but in an attempt to
keep the definition as generic as possible, the most apparent and definitely available
variables as input.

\begin{equation}
	dB\varepsilon_{cpp} =
10log_{10}\left(\frac{\frac{P_{total}}{N_{ports}}/Util_p*Speed_{max}}{kTln2}\right)
	\label{eq:energyefficiency_pp}
\end{equation}

Where \\
$dB\varepsilon$: absolute energy efficiency \\
$dB\varepsilon_{cpp}$: absolute current energy efficiency per port
\\
$P_{total}$: current total energy consumption of device \\
$N_{ports}$: number of ports \\
$S_{max}$: maximum speed of port in bits/second \\
$Util_p$: current port utilization \\
$k$: Boltzmann constant ($1.381 * 10^{-23} J/K$) \\
$T$: temperature in Kelvin \\
$kTln2$: absolute minimum energy per bit dissipated \\

If in future the distribution of energy profiling data is in place and more extensive
the following definition might be worth considering to replace aforementioned $\frac{P_{total}}{N_{ports}}$ with definition~\ref{eq:powerusage}. It makes use of baseline measurements of
devices~\citep{dimitar}. This would require to register baseline measurements for all devices or
global historical energy data from which the baseline could be derived. The former
represents a unfeasible overhead and the latter is not in place yet.

\begin{equation}
	P_{pp} = \frac{P_{tp} - P_{b}}{N_{p}}
	\label{eq:powerusage}
\end{equation}

Where \\
$P_{pp}$: estimated power per port \\
$P_{tp}$: average power for a specific throughput level \\
$P_{b}$: average baseline power \\
$N_{p}$: number of ports \\

A further consideration towards the future is taking advantage of the fact that the
derived metric includes the temperature $T$. Devices perform more or less
efficient according to their operation temperature. When temperature-sensor readings
get more widely available, they can be included in the calculation and thereby
yield more accurate values for the absolute energy efficiency.
